Locating the eigenvalues for graphs of small clique-width

Martin Fürer, Carlos Hoppen, David P. Jacobs, Vilmar Trevisan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

It is shown that if G has clique-width k, and a corresponding tree decomposition is known, then a diagonal matrix congruent to A- cI for constants c, where A is the adjacency matrix of the graph G of order n, can be computed in time O(k2n). This allows to quickly tell the number of eigenvalues in a given interval.

Original languageEnglish (US)
Title of host publicationLATIN 2018
Subtitle of host publicationTheoretical Informatics - 13th Latin American Symposium, Proceedings
EditorsMiguel A. Mosteiro, Michael A. Bender, Martin Farach-Colton
PublisherSpringer Verlag
Pages475-489
Number of pages15
ISBN (Print)9783319774039
DOIs
StatePublished - Jan 1 2018
Event13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 - Buenos Aires, Argentina
Duration: Apr 16 2018Apr 19 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10807 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th International Symposium on Latin American Theoretical Informatics, LATIN 2018
CountryArgentina
CityBuenos Aires
Period4/16/184/19/18

Fingerprint

Clique-width
Tree Decomposition
Congruent
Diagonal matrix
Adjacency Matrix
Eigenvalue
Decomposition
Interval
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Fürer, M., Hoppen, C., Jacobs, D. P., & Trevisan, V. (2018). Locating the eigenvalues for graphs of small clique-width. In M. A. Mosteiro, M. A. Bender, & M. Farach-Colton (Eds.), LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings (pp. 475-489). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10807 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-77404-6_35
Fürer, Martin ; Hoppen, Carlos ; Jacobs, David P. ; Trevisan, Vilmar. / Locating the eigenvalues for graphs of small clique-width. LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. editor / Miguel A. Mosteiro ; Michael A. Bender ; Martin Farach-Colton. Springer Verlag, 2018. pp. 475-489 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Fürer, M, Hoppen, C, Jacobs, DP & Trevisan, V 2018, Locating the eigenvalues for graphs of small clique-width. in MA Mosteiro, MA Bender & M Farach-Colton (eds), LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10807 LNCS, Springer Verlag, pp. 475-489, 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018, Buenos Aires, Argentina, 4/16/18. https://doi.org/10.1007/978-3-319-77404-6_35

Locating the eigenvalues for graphs of small clique-width. / Fürer, Martin; Hoppen, Carlos; Jacobs, David P.; Trevisan, Vilmar.

LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. ed. / Miguel A. Mosteiro; Michael A. Bender; Martin Farach-Colton. Springer Verlag, 2018. p. 475-489 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10807 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Fürer M, Hoppen C, Jacobs DP, Trevisan V. Locating the eigenvalues for graphs of small clique-width. In Mosteiro MA, Bender MA, Farach-Colton M, editors, LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. Springer Verlag. 2018. p. 475-489. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-77404-6_35